One weekend in April, 2010, 20,000 screaming and cheering fans showed up at the Georgia Dome in downtown Atlanta. The stadium is home to the Atlanta Falcons, a professional football team, but these fans weren’t cheering for their favorite football players. They were cheering for robots — and for the high school students who had built them.

Students on more than 300 teams from across the country had brought their homemade robots to Atlanta for the FIRST Robotics Championship. During the co...